Question
Use a graphing calculator to graph the original function y=12x−4
and the vertically dilated function with a factor k=6
. Determine the x-intercepts of both functions.(1 point)
Responses
The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (48,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 48 comma 0 right parenthesis .
The original function has an x-intercept of (−8,0)
, and the dilated function has an x-intercept of (−8,0)
.
The original function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis .
The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (8,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 8 comma 0 right parenthesis .
The original function has an x-intercept of (0,−4)
, and the dilated function has an x-intercept of (0,−24)
.
The original function has an x -intercept of left parenthesis 0 comma negative 4 right parenthesis , and the dilated function has an x -intercept of left parenthesis 0 comma negative 24 right parenthesis .
and the vertically dilated function with a factor k=6
. Determine the x-intercepts of both functions.(1 point)
Responses
The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (48,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 48 comma 0 right parenthesis .
The original function has an x-intercept of (−8,0)
, and the dilated function has an x-intercept of (−8,0)
.
The original function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis negative 8 comma 0 right parenthesis .
The original function has an x-intercept of (8,0)
, and the dilated function has an x-intercept of (8,0)
.
The original function has an x -intercept of left parenthesis 8 comma 0 right parenthesis , and the dilated function has an x -intercept of left parenthesis 8 comma 0 right parenthesis .
The original function has an x-intercept of (0,−4)
, and the dilated function has an x-intercept of (0,−24)
.
The original function has an x -intercept of left parenthesis 0 comma negative 4 right parenthesis , and the dilated function has an x -intercept of left parenthesis 0 comma negative 24 right parenthesis .
Answers
GPT-4o mini
To find the x-intercepts of the functions \( y = 12x - 4 \) and the vertically dilated function, we need to determine where each function equals zero.
1. **Original Function:**
\[
y = 12x - 4
\]
Set \( y \) to 0 to find the x-intercept:
\[
0 = 12x - 4
\]
\[
12x = 4
\]
\[
x = \frac{4}{12} = \frac{1}{3}
\]
So, the x-intercept of the original function is \( \left( \frac{1}{3}, 0 \right) \).
2. **Vertically Dilated Function:**
The vertically dilated function by a factor \( k = 6 \) would be:
\[
y = 6(12x - 4) = 72x - 24
\]
Set \( y \) to 0 to find the x-intercept:
\[
0 = 72x - 24
\]
\[
72x = 24
\]
\[
x = \frac{24}{72} = \frac{1}{3}
\]
So, the x-intercept of the dilated function is also \( \left( \frac{1}{3}, 0 \right) \).
Based on our calculations, **the x-intercepts for both functions are the same:**
\[
\left( \frac{1}{3}, 0 \right)
\]
Therefore, none of the provided response options are correct. The x-intercepts for both functions are at \( \left( \frac{1}{3}, 0 \right) \).
1. **Original Function:**
\[
y = 12x - 4
\]
Set \( y \) to 0 to find the x-intercept:
\[
0 = 12x - 4
\]
\[
12x = 4
\]
\[
x = \frac{4}{12} = \frac{1}{3}
\]
So, the x-intercept of the original function is \( \left( \frac{1}{3}, 0 \right) \).
2. **Vertically Dilated Function:**
The vertically dilated function by a factor \( k = 6 \) would be:
\[
y = 6(12x - 4) = 72x - 24
\]
Set \( y \) to 0 to find the x-intercept:
\[
0 = 72x - 24
\]
\[
72x = 24
\]
\[
x = \frac{24}{72} = \frac{1}{3}
\]
So, the x-intercept of the dilated function is also \( \left( \frac{1}{3}, 0 \right) \).
Based on our calculations, **the x-intercepts for both functions are the same:**
\[
\left( \frac{1}{3}, 0 \right)
\]
Therefore, none of the provided response options are correct. The x-intercepts for both functions are at \( \left( \frac{1}{3}, 0 \right) \).